Artist:Leonardo da Vinci (1452-1519) was revered by Renaissance contemporaries as a genius, yet also pitied as somehow frustrated: "unstable" as the 16th-century biographer Vasari bluntly put it, constantly having brilliant ideas that he lacked the will to execute.

This image of Leonardo the mental gadabout dissipated in the 19th century, when the sheer scale and precociousness of the Tuscan artist's research were recognised by scholars, who analysed his manuscript notes and were startled by the systematic nature of his anatomical, meteorological, engineering and art theories.

Whereas Vasari had seen a man flitting from one idea to another, modern culture celebrates Leonardo's as the supreme Renaissance mind, exploring scientific and aesthetic problems in parallel. Yet his melancholia haunts us.

Sigmund Freud's 1910 book Leonardo da Vinci and a Memory of His Childhood restates the older view of Leonardo and, although Freud's diagnosis rests on some dodgy translations, his stress on Leonardo's inability to finish convinced art historians such as Kenneth Clark and EH Gombrich that he had an irrational side.

It's true he didn't complete many of his large projects, preferring private research, but this withdrawal was his greatest contribution to our idea of art. In valuing drawing and experiments more than princes' commissions, Leonardo displayed his belief that art is autonomous mental labour rather than mere handicraft.

Subject: Leonardo's grotesque heads are a major part of his oeuvre. He drew them constantly, as doodles or as fully-fledged finished drawings of which this is the largest survivor. They are the most explicit way in which the most curious mind of the Renaissance addresses the irrational in himself. It resembles a confession. There is a story that it is a portrait of Scaramuccia, a Gypsy chieftain - a drawing by Leonardo that Vasari supposedly possessed. There is no proof. The angle of the face resembles that of Judas in Leonardo's Last Supper (1497).

Distinguishing features: He has a storm in him. His hair broils and rages like the sea. Leonardo, who repeatedly drew floods, gives this man's hair the tumult of waves smashing and rearing. Over his forehead, it forms into a whirlpool, a perfect, uncanny spiral at the heart of the waves, a vortex into his skull, seeming to suck the imagination into an obscure psychic interior. It suggests fear, dread - you don't want to know what's in there.

Under the mad sea of his hair, the back of his neck is overhung, deeply shaded. His ear is a black hole, a portal of the mind's melancholy realm. The eye we see bordered by lined and creased skin is softly drawn and sensitive. Under his beetling brow, it looks out observantly, even wisely - a human is inside this head.

His cheek, too, is an area of gentleness, shaded with a wonderful yielding texture, a calm plain between the tempestuous hair and the elephantine, mineral outgrowths of nose, lips and chin.

These are bulging, pushed-out, splayed-anatomy specimens of features, derangements of bone and muscle, the hooked nose almost noble compared with the gross protrusion of mouth and the iguana's flabby neck.

But the force of the drawing is centred in that whirlpool. The exterior absurdities tell us nothing about the more monstrous realm of the mind. The man's back is left unfinished as if this were a spontaneous sketch from life. According to Vasari, Leonardo used to stalk bizarre-looking people through Florence and later sketch them.

In his notebooks, Leonardo records seeing a prodigious-looking person in circumstances that suggest a research trip: "Giovannina - fantastic face - in the hospital of Saint Catherine's."

Inspirations and influences: The madness of this drawing anticipates Goya and the surrealists, in particular Ernst and Dali, both of whom consciously emulated Leonardo.